The area of the triangle formed by the tangen | vedclass

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(C) The equation of the tangent at $P(3, 4)$ to the circle ${x^2} + {y^2} = 25$ is given by $xx_1 + yy_1 = r^2$,which is $3x + 4y = 25$.To find the in

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$\frac{625}{24}$

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(C) The equation of the tangent at $P(3, 4)$ to the circle ${x^2} + {y^2} = 25$ is given by $xx_1 + yy_1 = r^2$,which is $3x + 4y = 25$.To find the intercepts on the coordinate axes,set $y = 0$ to get $3x = 25$,so $x = \frac{25}{3}$. Thus,the point $A$ is $(\frac{25}{3}, 0)$.Set $x = 0$ to get $4y = 25$,so $y = \frac{25}{4}$. Thus,the point $B$ is $(0, \frac{25}{4})$.The triangle formed by the tangent and the coordinate axes is a right-angled triangle $\Delta OAB$ with base $OA = \frac{25}{3}$ and height $OB = \frac{25}{4}$.Area of $\Delta OAB = \frac{1}{2} 	imes OA 	imes OB = \frac{1}{2} 	imes \frac{25}{3} 	imes \frac{25}{4} = \frac{625}{24}$.

The area of the triangle formed by the tangent at $(3, 4)$ to the circle ${x^2} + {y^2} = 25$ and the coordinate axes is

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